Question

The logical statement
represents the inverse of the conditional statement “If you are human, then you were born on Earth.”



Which statement is the converse?



Are the converse and the inverse true statements? Explain.

Answer 1

Let P = “you are human” and Q = “you were born on Earth.”
The original conditional is P → Q: “If you are human, then you were born on Earth.”

- The converse is Q → P: “If you were born on Earth, then you are human.”
- (The inverse, which your prompt gave, is ¬P → ¬Q: “If you are not human, then you were not born on Earth.”)

Are they true? No. Both the converse and the inverse are false. A counterexample is any non‑human animal (say, a dog): it was born on Earth (Q is true) but is not human (P is false). That makes Q → P false and also makes ¬P → ¬Q false.

Note: the converse and inverse always have the same truth value (they are logically equivalent to each other), but they are not generally equivalent to the original conditional. The contrapositive (¬Q → ¬P) would be equivalent to the original.